## Lecture series of the SFB CRC/TRR 191 "Symplectic Structures in Geometry, Algebra and Dynamics"

**10.10.2017 and 11.10.2017** Leonid Polterovich (Tel Aviv University), * Instabilities in Hamiltonian Dynamics and Symplectic Topology I, II.*

The first lecture will take place at 16:15 in NA 5/24 and the second one at 16:15 in NA 5/64.

** Abstract:**

In the 1st lecture, we discuss an existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. We show an application to superconductivity channels in nearly integrable systems (joint with Michael Entov).

In the 2nd lecture, we focus on applications of theory of persistence modules, an algebraic technique originated in topological data analysis, to geometry and dynamics of Hamiltonian diffeomorphisms (joint with Egor Shelukhin).